# Is there a smallest amount of (stuff) that can have hotness? **URL:** \ **Category:** Factual Questions\ **Created:** [April 2, 2014, 2:22pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166 "2014-04-02T14:22:04Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Chief\_Pedant](https://avatars.discourse-cdn.com/v4/letter/c/a6a055/32.png) [@Chief\_Pedant](https://boards.straightdope.com/u/Chief_Pedant)\ **Post date:** [April 2, 2014, 2:22pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/1 "2014-04-02T14:22:04Z")
I’m pretty sure I am too intellectually challenged to even phrase the question correctly, but I’m wondering if the concept of “temperature” has a lowest bound for the (quantity?) of (particles, maybe?) the “system” must contain in order for the concept of “temperature” to have meaning for it… I’m not drunk or anything…just stupid. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [April 2, 2014, 2:37pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/2 "2014-04-02T14:37:53Z")
Temperature of a parcel of matter is a manifestation of the average kinetic energy of its constituent atoms. In that sense, each atom in a gas cloud has its own temperature associated with how fast it’s moving. It’s not clear to me whether temperature can be associated with subatomic particles, i.e. electrons, protons, neutrons, etc. ---
**Author:** ![HoneyBadgerDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/honeybadgerdc/32/1033_2.png) [@HoneyBadgerDC](https://boards.straightdope.com/u/HoneyBadgerDC)\ **Post date:** [April 2, 2014, 2:48pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/3 "2014-04-02T14:48:27Z")
Thats a great question, I have wondered that many times myself. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 2, 2014, 2:54pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/4 "2014-04-02T14:54:21Z")
There’s a lower bound where the concept of temperature _can_ be used, and there’s a lower bound of where it _should_ be used. You _could_ use temperature to describe the state of any system composed of at least two particles. However, for such a simple system, it would also be practical, and much more useful, to describe the energies of all of the component particles independently. The concept of temperature is only useful for systems so complex that that’s no longer practical. ---
**Author:** ![PlainJain](https://avatars.discourse-cdn.com/v4/letter/p/5daacb/32.png) [@PlainJain](https://boards.straightdope.com/u/PlainJain)\ **Post date:** [April 2, 2014, 3:09pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/5 "2014-04-02T15:09:04Z")
> [@Chronos](#): > > The concept of temperature is only useful for systems so complex that that’s no longer practical. I don’t understand this sentence. Could you give an example? ---
**Author:** ![Don\_t\_Panic](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/don_t_panic/32/398_2.png) [@Don\_t\_Panic](https://boards.straightdope.com/u/Don_t_Panic)\ **Post date:** [April 2, 2014, 3:18pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/6 "2014-04-02T15:18:35Z")
> [@Chief\_Pedant](#): > > **Is there a smallest amount of (stuff) that can have hotness?** One Ellen Page? ---
**Author:** ![Grey](https://avatars.discourse-cdn.com/v4/letter/g/b782af/32.png) [@Grey](https://boards.straightdope.com/u/Grey)\ **Post date:** [April 2, 2014, 3:22pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/7 "2014-04-02T15:22:01Z")
> [@PlainJain](#): > > I don’t understand this sentence. Could you give an example? Think of temperature as a statistical measure of kinetic energy in a system of particles. A few particles can be discussed individually as **Chronos** mentioned but once you get up a few hundred or a few thousand, or a single mole (6.2x10[sup]23[/sup]), doing individual examinations is impractical. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [April 2, 2014, 3:30pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/8 "2014-04-02T15:30:18Z")
> [@Chronos](#): > > You _could_ use temperature to describe the state of any system composed of at least two particles. Just to clarify. Could you in theory assign a temperature to a hydrogen atom with a proton and electron? If you could do that, can you assign one to a proton made up of three quarks? I’m assuming the answer to each of these is no and that temperature is a classical notion and doesn’t really apply in situations where you’d be using quantum mechanics as your description. ---
**Author:** ![Chief\_Pedant](https://avatars.discourse-cdn.com/v4/letter/c/a6a055/32.png) [@Chief\_Pedant](https://boards.straightdope.com/u/Chief_Pedant)\ **Post date:** [April 2, 2014, 3:34pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/9 "2014-04-02T15:34:41Z")
> [@Chronos](#): > > There’s a lower bound where the concept of temperature _can_ be used, and there’s a lower bound of where it _should_ be used. You _could_ use temperature to describe the state of any system composed of at least two particles. However, for such a simple system, it would also be practical, and much more useful, to describe the energies of all of the component particles independently. The concept of temperature is only useful for systems so complex that that’s no longer practical. So…and apologies for the dullness…any given (small-enough) individual particle (say, for example, the elementary particles of the Standard Model) always has an absolute energy? That way, if you have two “systems” with two particles each, the one containing particles with more total energy could be said (even if it shouldn’t be said) to be the system with the higher temperature? And if that’s the case, would the (theoretically, thought experiment…) lowest temperature system then be the one containing two of the most weakly interacting particles (coupla electron neutrinos, maybe?)? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 2, 2014, 3:55pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/10 "2014-04-02T15:55:55Z")
You could assign a temperature to a hydrogen atom or baryon, but as I said before, the concept would be extremely unuseful. This is especially true since the energies are quantized, and in the case of a single baryon, the second-lowest energy state is so far above the lowest that it can usually be ignored completely. **PlainJane** , I realize on re-reading that that sentence of mine was ambiguous. If practical, you’d like to list the energies of each individual particle. If it’s not practical to list all those individual energies, then you instead just talk about the average energy, or temperature. I didn’t mean “if temperature is impractical you use temperature”. ---
**Author:** ![kenobi\_65](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kenobi_65/32/13178_2.png) [@kenobi\_65](https://boards.straightdope.com/u/kenobi_65)\ **Post date:** [April 2, 2014, 4:28pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/11 "2014-04-02T16:28:55Z")
> [@Martian Bigfoot](#): > > One Ellen Page? That is certainly the direction my brain took, though I was thinking more of Natalie Portman or Eva Longoria…but the point’s still there. 😃 ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [April 2, 2014, 4:34pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/12 "2014-04-02T16:34:11Z")
> [@OldGuy](#): > > Just to clarify. Could you in theory assign a temperature to a hydrogen atom with a proton and electron? If you could do that, can you assign one to a proton made up of three quarks? I’m assuming the answer to each of these is no and that temperature is a classical notion and doesn’t really apply in situations where you’d be using quantum mechanics as your description. It’s not that temperature is a _classical_ notion, it’s that temperature is a\* statistical \*notion. Temperature is essentially a measure of average kinetic energy per object, and when there are few enough objects, talking about the average isn’t very useful or make much sense. As an example, if you’re looking at all US adult males, knowing the average height could be useful – you’re designing seats for mass-produced cars or something. You certainly don’t want to go through all however many hundred million individually. But on the other hand, if you’re looking at three NBA players, their average height doesn’t really tell you much of interest; you’re going to consider them one at a time. You can in fact assign a temperature to a single molecule, if you know how fast it’s moving, but there’s no reason to. If there was some prediction you wanted to make that involved using temperature, it would be more accurate and easier to do the calculation right from the actual speed and other properties of the molecule without going through the statistical averaging inherent in temperature concepts. There’s no clear line where there are enough objects to make temperature a useful concept; it’s going to depend on the actual objects and what you want to do. Quantum effects make defining and calculating temperature a little more complicated, but most of the time if quantum effects matter significantly then you’re already looking at a system where temperature isn’t very useful anyway. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 2, 2014, 5:04pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/13 "2014-04-02T17:04:22Z")
It should also be mentioned that much of our theoretical framework for dealing with temperature depends on there being many particles. Yes, you have an average energy per particle, but you’ll have some above and below that energy, too. Give a system of particles a chance to settle into equilibrium, and there will be a very particular distribution of energies (what’s often called a thermal distribution). Thus, you can, for instance, say how many particles have 10% more energy than the average, or twice the average energy, or half the average energy. This is a very useful thing to be able to say about the system, since it lets us study things like evaporation or condensation. If you have a very simple system, though, with few particles, all of this statistical framework falls apart. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [April 2, 2014, 5:06pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/14 "2014-04-02T17:06:24Z")
> [@Quercus](#): > > Quantum effects make defining and calculating temperature a little more complicated, but most of the time if quantum effects matter significantly then you’re already looking at a system where temperature isn’t very useful anyway. Sometimes, but not always. For example, to explain the behavior of the specific heats of polyatomic gases (e.g., [hydrogen gas](http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html#c6)) as temperature increases, you have to take quantum mechanics into account. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [April 2, 2014, 6:00pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/15 "2014-04-02T18:00:20Z")
It’s an interesting question. I have to admit that I’m just taking a stab in the dark here, but it seems to me that a lot of the answer depends on how you define “temperature”. I’d be inclined to define it in terms of emission of thermal energy (or its logical converse, absorption thereof), which in the most general case really just means emission of radiation. My first guess would have characterized it in terms of the kinetic energy of molecules, but in fact if one thinks in terms of either [dipole radiation](http://en.wikipedia.org/wiki/Dipole#Dipole_radiation) or the photon emission of an accelerated charged particle, perhaps the smallest thing that can be characterized as having “temperature” is an electron. I stand willing to be corrected. P.S.- Ellen Page is cute but she is gay. Not that there’s anything wrong with that (the obligatory Seinfeld quote). 😃 ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [April 2, 2014, 6:09pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/16 "2014-04-02T18:09:27Z")
> [@Chronos](#): > > There’s a lower bound where the concept of temperature _can_ be used, and there’s a lower bound of where it _should_ be used. If you try define where that lower bound is, do you run into the [paradox of the heap](http://en.wikipedia.org/wiki/Sorites_paradox)? ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [April 2, 2014, 6:15pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/17 "2014-04-02T18:15:04Z")
The concept of temperature, as I’ve kinda-sorta managed to understand it from grade-school science lessons, seems to require a bunch of particles bouncing off of one another in some contained space – for example, a solid object in which the molecules are bound together by inter-molecular bonds, or a gas enclosed in a closed jar. Squeeze the jar, forcing the particles closer together, and they will bounce off each other a lot more, which we recognize as “getting hotter”. The physicist will explain this, I suppose, by saying the system has the same kinetic energy, now contained in a smaller volume; thus, temperature is a “kinetic energy density” sort of measure. I think that’s why **Chronos** says you need at least two particles. I understand that to mean, you need particles bouncing off one another before “temperature” is meaningful. If you have one lone particle, or even two particles or any number that aren’t contained, there is no temperature. Is this anywhere near right? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 2, 2014, 6:24pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/18 "2014-04-02T18:24:39Z")
You avoid the paradox of the heap the same way you avoid it in any other context: For a system that’s close to that fuzzy line, sometimes you’ll consider it a heap, and sometimes you won’t, depending on why you’re interested. You might, for instance, do thermal calculations on such a system while roughing it out on the back of a napkin at lunch, but then go back to work and model the system in detail on your computer. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 2, 2014, 6:28pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/19 "2014-04-02T18:28:18Z")
**Senegoid** , you can actually speak just fine of the temperature of a group of particles that aren’t interacting with each other at all, or which are interacting only extremely weakly or indirectly. Particles which don’t interact at all might or might not have a thermal distribution, and if they don’t, it’ll make the concept of temperature less useful, but it takes a surprisingly small amount of interaction to lead to thermalization. ---
**Author:** ![Yllaria](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yllaria/32/3452_2.png) [@Yllaria](https://boards.straightdope.com/u/Yllaria)\ **Post date:** [April 2, 2014, 7:04pm UTC](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166/20 "2014-04-02T19:04:14Z")
> [@wolfpup](#): > > . . . it seems to me that a lot of the answer depends on how you define “temperature”. I’d be inclined to define it in terms of emission of thermal energy (or its logical converse, absorption thereof), . . . Actually, if the temperature/energy is moving, the moving part is called heat. If you take thermodynamics, on the first day there will be much defining of terms. You will be told that the phrase ‘heat transfer’ is redundant because if there is no transfer, you can’t call it heat. Which will be amusing if the title of your textbook is\* Heat Transfer\*. [Next page](https://boards.straightdope.com/t/is-there-a-smallest-amount-of-stuff-that-can-have-hotness/685166.md?page=2)